Boris Kogan

Intracellular Ca2+ Dynamics and the Stability of Ventricular Tachycardia

Ventricular fibrillation (VF), the major cause of sudden cardiac death, is typically preceded by ventricular tachycardia (VT), but the mechanisms underlying the transition from VT to VF are poorly understood. Intracellular Ca(2+) overload occurs during rapid heart rates typical of VT and is also known to promote arrhythmias. We therefore studied the role of intracellular Ca(2+) dynamics in the transition from VT to VF, using a combined experimental and mathematical modeling approach. Our results show that 1) rapid pacing of rabbit ventricular myocytes at 35 degrees C led to increased intracellular Ca(2+) levels and complex patterns of action potential (AP) configuration and the intracellular Ca(2+) transients; 2) the complex patterns of the Ca(2+) transient arose directly from the dynamics of intracellular Ca(2+) cycling, and were not merely passive responses to beat-to-beat alterations in AP; 3) the complex Ca(2+) dynamics were simulated in a modified version of the Luo-Rudy (LR) ventricular action potential with improved intracellular Ca(2+) dynamics, and showed good agreement with the experimental findings in isolated myocytes; and 4) when incorporated into simulated two-dimensional cardiac tissue, this action potential model produced a form of spiral wave breakup from VT to a VF-like state in which intracellular Ca(2+) dynamics played a key role through its influence on Ca(2+)-sensitive membrane currents such as I(Ca), I(NaCa), and I(ns(Ca)). To the extent that spiral wave breakup is useful as a model for the transition from VT to VF, these findings suggest that intracellular Ca(2+) dynamics may play an important role in the destabilization of VT and its degeneration into VF.

The simplified-FitzHugh-Nagumo model with action potential duration restitution: effects on 2D wave propagation

Abstract A modification of the simplified FitzHugh-Nagumo (FN) equations is proposed for introducing a residual component of the slow variable, which determines the restitution of action potential duration (APD) also known as the interval-excitation duration relationship. The three-step-wise approximation of ϵ( E ) which is widely used in current publications is replaced in a new model by a four-step approximation. This change is used for studying by computer simulation the effects of APD restitution properties independently of the APD and refractory period on 2D wave propagation in an isotropic matrix (made by 128 × 128 nodes). The method for fitting the model to the given experimental restitution data (obtained from myocardial cells) is presented. The computer simulations implemented on a massively parallel computer (Connection Machine) showed at least three important qualitative distinctions in behavior which demonstrate the effect of APD restitution: changes in the speed and wavelength of propagated waves with the period of stimulation, non-stationary propagation of spiral waves, and site-specific induction of spiral waves with premature stimulation not on the tail of the previous wave. Quantitative effects of differing restitution properties are expressed in the size and location of a window of vulnerability in 2D excitable media. These windows are characterized by the appearance of single and double spiral waves in response to premature stimulation applied inside the window. Thus the APD restitution incorporated in the FN model produces a significant effect on the formation and propagation of spiral waves.

Excitation wave propagation within narrow pathways: geometric configurations facilitating unidirectional block and reentry

Abstract The propagation of excitation waves in narrow pathways of 2D excitable media through regions of impermeable media and decreased excitability media is investigated as a model of reentrant arrhythmias in the heart. Arrhythmia occurrences are common in the presence of infarct scars where regions of normal tissue are interspersed with inexcitable ones. Propagation through narrow pathways with three idealized geometric configurations are considered: propagation through narrow paths with either parallel borders, tapered borders, or a combination of these. The focus of this study is on the conditions for unidirectional block and reentry appearance. It is shown that in narrow paths with only parallel borders unidirectional block is impossible, regardless of the properties of the border media. In this case only bidirectional propagation or block is possible, depending on the pathway width. Unidirectional block can occur, however, when the narrow path has a tapered shape. Waves propagating from the wide end of the pathway die out at the narrow end, while waves propagating in the opposite direction are able to pass through. An approximate relationship between the geometry of the pathway and wave front curvature is obtained. This provides a simple approach to estimate the critical curvature value in computer simulations of various excitable media or in experiments with real media. A new computer simulation approach is proposed to closely approximate the dependence of stationary speed of propagation on wave front curvature. In computer simulations of a two dimensional grid of 128 × 128 membrane segments, using the modified FitzHugh-Nagumo equations, the arrangement of two or more pathways in parallel permits reentry if at least one pathway has a configuration causing unidirectional block, and the medium at the site of unidirectional block has sufficient time to recover from the previous excitation. The latter is facilitated by anisotropic conduction properties of the media especially in the case with impermeable borders. Thus, there exist specific geometric configurations of two dimensional narrow pathways, which allow reentry even when the media properties are uniform.

Wave propagation in cardiac tissue and effects of intracellular calcium dynamics (computer simulation study)

Computer simulation using Luo-Rudy I1 model of ventricular myocyte showed that intracellular calcium dynamics become irregular in case of high rate stimulation. This causes the transition from stationary to nonstationary spiral wave and its breakup in 2D model of cardiac tissue. Obtained results suggest how ventricular fibrillation may occur due to the abnormalities of intracellular calcium dynamics. The short review of existing cardiac cell models with calcium dynamics is presented.

Simulation of nonlinear distributed parameter systems on the connection machine

The recently introduced Connection Machine, CM-2, is a multiprocessor with massive parallelism. Fully expanded, the CM-2 consists of 64K processing elements connected in a hypercube topology. Each processing element contains a single-bit arithmetic and logic unit as well as up to 256K bits of local memory. Operation is in the SIMD mode with a single control unit controlling all the processors. In this paper the application of a quarter CM-2 (16K processing elements) to the simulation of excitable media is described. Excitable media are distributed parameter systems, charac terized by nonlinear partial differential equations, containing distributed sources of energy. Excitable media arise in biological systems (e.g. heart muscles), chemical processes and a variety of other application areas. The implementation of a mathematical model for the heart muscle on the CM-2 permitted the generation of very interesting computational results.

Tachycardia-induced early afterdepolarizations: Insights into potential ionic mechanisms from computer simulations

Although early afterdepolarizations (EADs) are classically thought to occur at slow heart rates, mounting evidence suggests that EADs may also occur at rapid heart rates produced by tachyarrhythmias, due to Ca overload of the sarcoplasmic reticulum (SR) leading to spontaneous SR Ca release. We hypothesized that the mechanism of tachycardia-induced EADs depends on the spatial and temporal morphology of spontaneous SR Ca release, and tested this hypothesis in computer simulations using a ventricular action potential mathematical model. Using two previously suggested spontaneous release morphologies, we found two distinct tachycardia-induced EAD mechanisms: one mechanistically similar to bradycardia-induced EADs, the other to delayed afterdepolarizations (DADs).

The application of a massively parallel computer to the simulation of electrical wave propagation phenomena in the heart muscle using simplified models

The simulation of heart arrhythmia and fibrillation are very important and challenging tasks. The solution of these problems using sophisticated mathematical models is beyond the capabilities of modern supercomputers. To overcome these difficulties, it is proposed to break the whole simulation problem into two tightly coupled stages: generation of the action potential using sophisticated models, and propagation of the action potential using simplified models. The well-known simplified models are compared and modified to bring the rate of depolarization and action potential duration restitution closer to reality. The modified method of lines is used to parallelize the computational process. The conditions for the appearance of 2D spiral waves after the application of a premature beat and the subsequent traveling of the spiral wave inside the simulated tissue are studied.<<ETX>>

Visualization of wave propagation through a 3D strand of myocardium

The authors present recent results obtained from simulating the action potential generation and propagation through a thin 3-D cylindrical heart muscle bundle. These results represent the first step towards obtaining a more accurate understanding of wave propagation properties through striated muscles. Using a 3-D computational grid of 32*32*128 cells, a single muscle bundle was modeled. The individual fibers and inter-fiber matter making up the bundle were treated homogeneously. Using a modified FitzHugh-Nagumo equation called the Epsilon-4 model, the authors obtained the relationship of propagation speed as a function of cross-sectional depth. The variations in speed that were observed can be explained in terms of the different wave curvatures arising from different types of boundary conditions and the geometry of the pathway. From these observations, the authors construct experiments where unidirectional blocks can occur in geometries with low excitability and no flux borders.<<ETX>>

Excitation wave front transients: a computer simulation study

The propagation of excitation waves in narrow pathways of 2-0 excitable media through regions of impermeable and decreased excitability is investigated as a model of cardiac reentrant arrhythmias. Transient phenomena in wave front formation are studied at the entrance and exits of these pathways. Computer simulation uncovered these phenomena for paths with two geometric configurations (parallel and tapered borders), two types of borders (impermeable and with decreased excitability), and two types of viable tissue (isotropic and anisotropic). We show that under certain conditions these transients can lead to the slow-down of propagation and unidirectional block.